U novoj peći kruh je gotov brže nego u staroj.

Because u can mean either in or into, depending on the case:

• u + locative = location, in
• u + accusative = movement toward something, into

So:

• u novoj peći = in the new oven
• u novu peć = into the new oven

In this sentence, we are talking about where the bread becomes ready, so Croatian uses the locative.

They are both feminine singular locative forms.

The noun peć is feminine, so the adjectives have to agree with it:

• nova peć = a new oven
• u novoj peći = in the new oven

Likewise:

• stara peć = an old oven
• u staroj peći = in the old oven

So novoj and staroj are simply the locative forms of nova and stara.

No. Here peći is the noun peć in the locative singular.

That can be confusing, because peći is also the infinitive of the verb to bake. But in this sentence, the preposition u tells you that a noun phrase is coming:

• u novoj peći = in the new oven

So this peći means oven, not to bake.

Because Croatian often leaves out a noun when it is already obvious from context.

So:

• u novoj peći ... nego u staroj really means
• u novoj peći ... nego u staroj peći

English does the same thing sometimes:

• in the new oven ... than in the old one

Croatian just omits the repeated noun more directly.

Literally, it means the bread is ready or the bread is done.

In the context of food, gotov often means:

• finished
• done
• ready

So here kruh je gotov means that the bread has finished baking and is ready.

Because gotov has to agree with kruh.

The noun kruh is masculine singular, so the adjective must also be masculine singular:

• kruh → masculine singular
• gotov → masculine singular

If the noun were feminine, you would use gotova. If it were neuter, you would use gotovo.

Because brže is an adverb, while brži is an adjective.

Here Croatian is comparing how quickly the bread becomes ready, not describing the bread itself as faster.

• brz = fast
• brži = faster (adjective)
• brzo = quickly
• brže = more quickly / faster (adverb)

So:

• kruh je gotov brže = the bread is ready faster / more quickly

That is why brže is the correct form.

Nego is the normal word for than after a comparative in sentences like this.

So:

• brže nego u staroj = faster than in the old one

Croatian also uses od with comparisons, but that is more common when comparing directly with a noun phrase:

• brži od vlaka = faster than a train

In this sentence, nego is the natural choice because the second part is really an abbreviated comparison:

• nego u staroj peći

Yes, Croatian word order is fairly flexible, but je is a clitic, and clitics usually go in second position in their clause.

So kruh je gotov is a very normal, neutral order.

Other orders are possible, but they change the emphasis a bit:

• Kruh je gotov = neutral
• Gotov je kruh = more marked, with emphasis on gotov

For learners, kruh je gotov is the safest and most natural pattern to copy.

Because Croatian does not have articles like English a and the.

So a noun like kruh can mean:

• bread
• the bread
• a bread

The exact meaning depends on context.

The same applies to:

• u novoj peći = in a new oven / in the new oven
• u staroj = in an old one / in the old one

English has to choose an article, but Croatian usually does not mark that explicitly.